Sports a pennant for the sports teams at lincoln high school is in the shape of an isosceles triangle. if the measure of the vertex angle is 18, find the measure of each base angle.

Answer-

[tex]\boxed{\boxed{y^{\circ}=26^{\circ}\ 45'}}[/tex]

Solution-

As the triangle ABC is an isosceles triangle, with AC = BC.

So the angles A and B will be same, i.e

[tex]\Rightarrow \angle A=\angle B[/tex]

[tex]\Rightarrow 34^{\circ}=(x-5)^{\circ}[/tex]

[tex]\Rightarrow x^{\circ}=34^{\circ}+5^{\circ}[/tex]

[tex]\Rightarrow x^{\circ}=39^{\circ}[/tex]

As sum of all angles in a triangle is 180°, so

[tex]\Rightarrow \angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]\Rightarrow 34^{\circ}+39^{\circ}+4y^{\circ}=180^{\circ}[/tex]

[tex]\Rightarrow 4y^{\circ}=180^{\circ}-34^{\circ}-39^{\circ}[/tex]

[tex]\Rightarrow 4y^{\circ}=107^{\circ}[/tex]

[tex]\Rightarrow y^{\circ}=\dfrac{107^{\circ}}{4}[/tex]

[tex]\Rightarrow y^{\circ}=26.75^{\circ}[/tex]

[tex]\Rightarrow y^{\circ}=26^{\circ}\ 45'[/tex]

Answer:

[tex]h=\frac{25}{b+r}[/tex]

Step-by-step explanation:

Given equation,

[tex]bh+hr=25[/tex]

For solving this equation for h,

We need to isolate h in the left side of the equation,

We can write,

[tex]h(b+r) = 25[/tex]    ( by the converse of distributive property ),

Divide both sides by b + r,

[tex]h=\frac{25}{b+r}[/tex]

Which is the required equation.

To evaluate (4/9)^1/2, you find the square root of 4, which is 2, and the square root of 9, which is 3, hence the result is 2/3.

The student has asked to evaluate the expression (4/9)^1/2. To do this, you take the square root of both the numerator and the denominator separately. The square root of 4 is 2 and the square root of 9 is 3, therefore, the evaluation of the expression (4/9)^1/2 is equivalent to 2/3.

The angle measures 40 degrees, and its complement, which is 25% larger than the angle, measures 50 degrees. This is solved using elementary algebra by setting up an equation with the angle as 'x' and its complement as '90-x', and then simplifying the equation to solve for 'x'.

The question involves finding the measure of an angle and its complement when given that the complement exceeds the measurement of the angle by 25%. To solve this, let's use algebra. Let the measure of the angle be x degrees.

Since the complement of an angle adds up to 90 degrees with the angle itself, the complement can be represented as 90 - x degrees. According to the problem, the complement is 25% more than the angle, so we can write the equation:

90 - x = x + 0.25x

Simplifying, we get:

90 - x = 1.25x

90 = 2.25x

Dividing both sides by 2.25 gives us the measure of the angle x:

x = 40 degrees

Since the complement is 90 - x, we find:

Complement = 90 - 40 = 50 degrees

Therefore, the angle measures 40 degrees, and its complement measures 50 degrees.

When cosθ >0 then , b² + c² > a².

" Triangle is a 2 dimensional shape which is having three sides and three vertices. Sum of all the interior angles of a triangle is 180°."

Formula used

As per Cosine Rule

For a given ΔABC,

cosθ = [tex]\frac{b^{2} + c^{2} - a^{2} }{2bc}[/tex]

According to the question,

cosθ >0

⇒ [tex]\frac{b^{2} + c^{2}-a^{2} }{2bc}[/tex] >0

⇒ b² + c² >a²

Hence, we conclude that Option D is correct.

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Answer:

c

Step-by-step explanation:

To solve the system by substitution, substitute the value of z in the equations and solve them simultaneously.

To solve the system by substitution, we need to substitute the value of z in the other equations. Given that z=5, we can substitute this value in the first and third equations:

2x - y + 5 = -4

-2x + 3y - 5 = 10

Now, we can solve these two equations simultaneously to find the values of x and y.

To solve a system of equations by substitution, express one variable in terms of the other and substitute it into the other equations to eliminate that variable before solving for the remaining variables.

To solve this system of equations by substitution:

By following these steps, you can find the values of x, y, and z that satisfy the system of equations.

Given:

The temperature is given in Fahrenheit (13 degree F).

To Find:

The correct temperature in Celsius.

Answer:

The temperature in Celsius is approximately -11 degree C.

Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.

Step-by-step explanation:

Any temperature can be changed from F to C by using the formula

[tex]C=(\frac{5}{9})(F-32)\\\\C=\frac{5(F-32)}{9}[/tex]

So, we will convert the given temperature in F to C by performing three simple steps.

Step 1 - We will subtract 32 from the Fahrenheit temperature.

Step 2 - Multiply this number by 5.

Step 3 - Divide the resulting number by 9.

So,

Step 1: 13-32 = -19

Step 2: -19*5 = -95

Step 3: -95/9 = -10.55 approx

Thus, the temperature in Celsius is approximately -11 degree C.

Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.

Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.

Given:

Kyle is converting 13°F to °C.

The formula used to convert F to C is

C= 5/9 (F- 32)

Now, Substitute F= 13 into the formulas as

C=  5/9 (13 - 32)

C = 5/9 (-19)

C= -95/ 9

C= -10.55

Thus, the temperature in Celsius is -11 degree C.

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Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

If Jolinda scored 21 points of 28 total, the fraction is:

[tex]\frac{21}{28}=\frac{3}{4}= 0.75(or75\%)[/tex]

Remember that a fraction is the representation of a portion among the total.

In addition, this fraction also would represent the effectiveness of Jolinda, we could say that she is able to score a 75% of team's points.

Answer:

D) 4 7/10

Step-by-step explanation:

Any fraction may be written as a mixed number. This type of number is formed by one or more whole parts plus a fractional part.

4.7 = 4 + 0.7

4 + 7/10

4 7/10

Following this same reasoning we can turn a mixed number into improper fraction and improper fraction into mixed number.

ratio is 5:4

5+4 =9

54 pounds divided by 9 = 6

6*5 = 30

6*4 = 24

Sam gets 30 pounds Bethan gets 24 pounds

The correct expression representing the volume of the pyramid is:

[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]. Therefore the correct option is 2.

The volume [tex]\( V \)[/tex] of a pyramid is given by the formula:

[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]

For a square pyramid, the base area is given by [tex]\( \text{Base Area} = \text{side length}^2 \)[/tex].

In this case, the side length is [tex]\( x \)[/tex] and the height is [tex]\( y \)[/tex]. Therefore, the expression for the volume [tex]\( V \)[/tex] is:

[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]

Now, let's compare this with the given options:

1. [tex]\( \frac{1}{3}xy \)[/tex] cm³

2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³

3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³

4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³

Now, we can see that the correct expression representing the volume of the pyramid is:

[tex]\[ \frac{1}{3}x^2y \, \text{cm}^3 \][/tex]

So, the correct option is option 2: [tex]\( \frac{1}{3}x^2y \)[/tex] cm³.

The correct expression representing the volume of the pyramid is:

[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]

Complete question:

A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?

1. [tex]\( \frac{1}{3}xy \)[/tex] cm³

2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³

3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³

4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³

The area of a rectangular backdrop is 18.75 square feet and container has enough paint.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Given that, the rectangular backdrop is 60 inches by 45 inches.

We know that, 1 feet =12 inches

So, 60 inches = 60/12 = 5 inches

45 inches = 45/12 = 3.75 inches

Here, Area = 5×3.75

= 18.75 square feet

If his container of paint can cover 25 square feet.

So, Jose has enough paint.

Therefore, the area of a rectangular backdrop is 18.75 square feet and container has enough paint.

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